Spin-Charge separation in a model of two coupled chains

TL;DR

This paper exactly solves a two-chain electron model with bosonization, revealing how inter-chain hopping affects Fermi surface shape and electron correlations, leading to distinct regimes of spin-charge separation and inter-chain effects.

Contribution

It provides an exact solution showing the impact of transverse hopping on Fermi surface and electron excitations in coupled chains, highlighting different regimes of behavior.

Findings

Inter-chain hopping modifies Fermi surface shape.

Two regimes: short-distance insensitivity and long-distance relevance of t_perp.

Additional singularities in Green function at large distances.

Abstract

A model of interacting electrons living on two chains coupled by a transverse hopping $t_\perp$, is solved exactly by bosonization technique. It is shown that $t_\perp$ does modify the shape of the Fermi surface also in presence of interaction, although charge and spin excitations keep different velocities $u_\rho$, $u_\sigma$. Two different regimes occur: at short distances, $x\ll \xi = (u_\rho - u_\sigma)/4t_\perp$, the two chain model is not sensitive to $t_\perp$, while for larger separation $x\gg \xi$ inter--chain hopping is relevant and generates further singularities in the electron Green function besides those due to spin-charge decoupling. (2 figures not included. Figure requests: FABRIZIO@ITSSISSA)